Abstract: In arid areas, mid-long term runoff forecasting is very important for water resources planning and management. Because river runoff series has both randomness and gray characteristics, in China, the gray theory was used for forecasting runoff firstly in the late 1980s, and Markov prediction was used for forecasting runoff beginning this century. For long time series and large random fluctuations series, the prediction effect of gray model was poor and had lower accuracy. Meanwhile, Markov prediction model need data of random and long time series. Both forecasting methods are highly complementary. Therefore, in order to predict the mid-long term annual runoff, some studies had constructed GM(1, 1)-Markov prediction model by combining the gray system theory with Markov prediction. Compared with GM(1, 1)model, GM(1, 2)model introduced a reference series, which have a strong association with the main series. So GM(1, 2)model can improve the prediction accuracy of volatility series. In this paper, a GM(1, 2)-Markov prediction model was proposed. The paper constructed a GM(1, 2)-Markov prediction model for Zhengyixia Station based on data of the Heihe River, Gansu Province, China. Firstly, the annual runoff correlation between Zhengyixia Station and Yingluoxia Station of the Heihe River during the period 1949-2014 was analyzed. The annual runoff between Zhengyixia Station and Yingluoxia Station has a strong correlation. So the data of Yingluoxia Station acted as relevant factor data columns, and the data of Zhengyixia Station acted as controlling factors data columns to construct GM(1, 2)prediction model. Afterwards, the GM(1, 2)-Markov prediction model was established based on the annual runoff data from 1990 to 2009, and this model was verified with the annual runoff data from 2010 to 2014. In order to verify the merits of the GM(1, 2)-Markov model, using the same data to establish Zhengyixia's annual runoff both GM(1, 1)prediction model, and GM(1, 2)prediction model. The GM(1, 2)-Markov model was then compared with two other methods. To GM(1, 1)model, GM (1, 2)model and GM(1, 2)-Markov model of Zhengyixia's annual runoff prediction, the model accuracy of 83.83%, 82.62% and 83.65% were obtained respectively. Corresponding the next 5 years(2010-2014)prediction accuracy of 82.44%, 95.75% and 97.12% were obtained respectively. It means that the model accuracy of GM(1, 2)-Markov model, GM(1, 1)model and GM(1, 2)model are meet with the modeling requirements. However, prediction accuracy of GM(1, 2)-Markov model are higher than that of GM(1, 1)model and GM(1, 2)model. The results show that the GM(1, 2)-Markov model has the highest prediction accuracy compared to other models. This paper firstly proposed the GM(1, 2)-Markov model for mid-long term runoff forecasting in the relating research fields. The GM(1, 2)-Markov prediction model not only provides a new scientific method for annual river runoff of the mid- and long-term prediction, but also extends the applications range of Markov prediction and grey theory.

Key words: annual runoff, mid-long term prediction, GM(1, 2)model, Markov prediction, Zhengyixia Station